Math Problem Solver

Roots

\[\sqrt{90 \cdot {a}^{3} \cdot {b}^{6}} = i \sqrt[4]{8100 \left(\operatorname{re}{\left(a^{3} b^{6}\right)}\right)^{2} + 8100 \left(\operatorname{im}{\left(a^{3} b^{6}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(90 \operatorname{im}{\left(a^{3} b^{6}\right)},90 \operatorname{re}{\left(a^{3} b^{6}\right)} \right)}}{2} \right)} + \sqrt[4]{8100 \left(\operatorname{re}{\left(a^{3} b^{6}\right)}\right)^{2} + 8100 \left(\operatorname{im}{\left(a^{3} b^{6}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(90 \operatorname{im}{\left(a^{3} b^{6}\right)},90 \operatorname{re}{\left(a^{3} b^{6}\right)} \right)}}{2} \right)} \approx 9.48683298050514 i \left(\left(\operatorname{re}{\left(a^{3} b^{6}\right)}\right)^{2} + \left(\operatorname{im}{\left(a^{3} b^{6}\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(90 \operatorname{im}{\left(a^{3} b^{6}\right)},90 \operatorname{re}{\left(a^{3} b^{6}\right)} \right)}}{2} \right)} + 9.48683298050514 \left(\left(\operatorname{re}{\left(a^{3} b^{6}\right)}\right)^{2} + \left(\operatorname{im}{\left(a^{3} b^{6}\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(90 \operatorname{im}{\left(a^{3} b^{6}\right)},90 \operatorname{re}{\left(a^{3} b^{6}\right)} \right)}}{2} \right)}\]\[\sqrt{90 \cdot {a}^{3} \cdot {b}^{6}} = i \left(- \sqrt[4]{8100 \left(\operatorname{re}{\left(a^{3} b^{6}\right)}\right)^{2} + 8100 \left(\operatorname{im}{\left(a^{3} b^{6}\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(90 \operatorname{im}{\left(a^{3} b^{6}\right)},90 \operatorname{re}{\left(a^{3} b^{6}\right)} \right)}}{2} \right)}\right) - \sqrt[4]{8100 \left(\operatorname{re}{\left(a^{3} b^{6}\right)}\right)^{2} + 8100 \left(\operatorname{im}{\left(a^{3} b^{6}\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(90 \operatorname{im}{\left(a^{3} b^{6}\right)},90 \operatorname{re}{\left(a^{3} b^{6}\right)} \right)}}{2} \right)} \approx - 9.48683298050514 i \left(\left(\operatorname{re}{\left(a^{3} b^{6}\right)}\right)^{2} + \left(\operatorname{im}{\left(a^{3} b^{6}\right)}\right)^{2}\right)^{0.25} \sin{\left(\frac{\operatorname{atan_{2}}{\left(90 \operatorname{im}{\left(a^{3} b^{6}\right)},90 \operatorname{re}{\left(a^{3} b^{6}\right)} \right)}}{2} \right)} - 9.48683298050514 \left(\left(\operatorname{re}{\left(a^{3} b^{6}\right)}\right)^{2} + \left(\operatorname{im}{\left(a^{3} b^{6}\right)}\right)^{2}\right)^{0.25} \cos{\left(\frac{\operatorname{atan_{2}}{\left(90 \operatorname{im}{\left(a^{3} b^{6}\right)},90 \operatorname{re}{\left(a^{3} b^{6}\right)} \right)}}{2} \right)}\]